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- Satisfiability abstract "In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation (model) that makes the formula true. A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false. These four concepts are related to each other in a manner exactly analogous to Aristotle's square of opposition.The four concepts can be raised to apply to whole theories: a theory is satisfiable (valid) if one (all) of the interpretations make(s) each of the axioms of the theory true, and a theory is unsatisfiable (invalid) if all (one) of the interpretations make(s) each of the axioms of the theory false.It is also possible to consider only interpretations that make all of the axioms of a second theory true. This generalization is commonly called satisfiability modulo theories.The question whether a sentence in propositional logic is satisfiable is a decidable problem. In general, the question whether sentences in first-order logic are satisfiable is not decidable. In universal algebra and equational theory, the methods of term rewriting, congruence closure and unification are used to attempt to decide satisfiability. Whether or not a particular theory is decidable or not depends whether or not the theory is variable-free or on other conditions.".
- Satisfiability wikiPageID "23401166".
- Satisfiability wikiPageRevisionID "592164381".
- Satisfiability hasPhotoCollection Satisfiability.
- Satisfiability subject Category:Concepts_in_logic.
- Satisfiability subject Category:Logical_truth.
- Satisfiability subject Category:Model_theory.
- Satisfiability subject Category:Philosophy_of_logic.
- Satisfiability comment "In mathematical logic, satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation (model) that makes the formula true. A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and invalidity, that is, a formula is unsatisfiable if none of the interpretations make the formula true, and invalid if some such interpretation makes the formula false.".
- Satisfiability label "Erfüllbarkeit".
- Satisfiability label "Satisfaisabilité".
- Satisfiability label "Satisfatibilidade".
- Satisfiability label "Satisfiability".
- Satisfiability label "Spełnialność formuł logicznych".
- Satisfiability label "Vervulbaarheid".
- Satisfiability sameAs Splnitelnost.
- Satisfiability sameAs Erfüllbarkeit.
- Satisfiability sameAs Satisfaisabilité.
- Satisfiability sameAs Vervulbaarheid.
- Satisfiability sameAs Spełnialność_formuł_logicznych.
- Satisfiability sameAs Satisfatibilidade.
- Satisfiability sameAs m.06w7sm3.
- Satisfiability sameAs Q1350299.
- Satisfiability sameAs Q1350299.
- Satisfiability wasDerivedFrom Satisfiability?oldid=592164381.
- Satisfiability isPrimaryTopicOf Satisfiability.